To determine how much water would be required to fully dissolve 11 grams of calcium carbonate given that the solubility is [tex]\(14 \frac{\text{milligrams}}{\text{liter}}\)[/tex], we follow these steps:
1. Convert grams to milligrams:
Since 1 gram is equal to 1000 milligrams, we need to convert 11 grams of calcium carbonate to milligrams:
[tex]\[ 11 \text{ grams} = 11 \times 1000 \text{ milligrams} = 11,000 \text{ milligrams} \][/tex]
2. Determine the amount of water required:
Knowing that the solubility is [tex]\(14 \text{ milligrams per liter}\)[/tex], we can set up the ratio:
[tex]\[ \text{Amount of water required in liters} = \frac{\text{Amount of calcium carbonate in milligrams}}{\text{Solubility in milligrams per liter}} \][/tex]
Substituting in the given values:
[tex]\[ \text{Amount of water required} = \frac{11,000 \text{ milligrams}}{14 \text{ milligrams per liter}} \][/tex]
3. Calculate the answer:
[tex]\[ \text{Amount of water required} = 785.7142857142857 \text{ liters} \][/tex]
4. Express the answer with the correct number of significant figures:
The solubility and the amount of calcium carbonate given have 2 significant figures, so we should express our answer to 2 significant figures as well:
[tex]\[ \text{Amount of water required} \approx 790 \text{ liters} \][/tex]
Therefore, it would take [tex]\(790\)[/tex] liters of water to fully dissolve [tex]\(11\)[/tex] grams of calcium carbonate.
